6.1 And 6.2 Quiz - Polygons

Explanation
A do-decagon is a polygon with 12 sides. The prefix "do-" in do-decagon means 2, so it is a 2-decagon, which is equivalent to a 12-sided polygon.

Explanation
A regular polygon has congruent sides, meaning that all of its sides are of equal length. It also has congruent angles, meaning that all of its angles are of equal measure. Additionally, a regular polygon has the same shape, meaning that if you were to rotate, reflect, or resize it, it would still look exactly the same. Therefore, all three statements (I, II, and III) are true for a regular polygon.

Explanation
A stop sign has the same shape as an octagon. The stop sign is a red, eight-sided polygon with white letters that spell out "STOP." The octagonal shape of the stop sign is designed to make it easily recognizable and distinguishable from other signs on the road. The unique shape helps drivers quickly identify and respond to the sign, indicating that they must come to a complete stop at that intersection.

Explanation
The figure can be described as a convex polygon because all of its interior angles are less than 180 degrees and all of its sides are straight. Additionally, it can be described as a pentagon because it has five sides.

Explanation
The interior angle sum of a polygon can be found by using the formula (n-2) * 180, where n is the number of sides of the polygon. In the case of a pentagon, which has 5 sides, the interior angle sum would be (5-2) * 180 = 3 * 180 = 540. Therefore, the correct answer is 540.

Explanation
A convex polygon is a polygon in which all of its interior angles are less than 180 degrees. The sum of the interior angles of a convex polygon can be calculated using the formula (n-2) * 180, where n is the number of sides of the polygon. In this case, if the interior angle sum is 900 degrees, we can set up the equation (n-2) * 180 = 900. Solving for n, we get n = 7. Therefore, the convex polygon has 7 sides.

Explanation
A regular hexagon has six sides of equal length and six equal interior angles. To find the measure of each interior angle, we can divide the sum of all interior angles (which is 720 degrees) by the number of angles (which is 6). Therefore, each interior angle of a regular hexagon measures 720/6 = 120 degrees.

Explanation
A regular octagon has 8 sides, and the sum of the interior angles of any polygon can be found using the formula (n-2) * 180, where n is the number of sides. So, for an octagon, the sum of the interior angles is (8-2) * 180 = 1080 degrees. Since all the interior angles of a regular polygon are equal, we can divide the sum by the number of angles to find the measure of each angle. Therefore, each interior angle of a regular octagon is 1080/8 = 135 degrees.

Explanation
The exterior angle sum of any polygon is always 360 degrees. In a pentagon, there are five exterior angles, and when you add them all together, they will always equal 360 degrees. This is a property of polygons, where the sum of the exterior angles is always equal to 360 degrees.

Explanation
A regular polygon is a polygon with all sides and angles equal. Since the exterior angle of the regular polygon is given as 60 degrees, we can determine the number of sides by using the formula: 360 degrees divided by the measure of each exterior angle. In this case, 360 degrees divided by 60 degrees equals 6. Therefore, the regular polygon has 6 sides, making it a hexagon.

Explanation
The exterior angle of a regular polygon is formed by extending one side of the polygon. In a regular polygon, all exterior angles are equal. Since one exterior angle is given as 20 degrees, we can determine the number of sides by dividing 360 degrees (the sum of all exterior angles of any polygon) by 20 degrees. 360 degrees divided by 20 degrees equals 18 sides. Therefore, the correct answer is 18.

Explanation
Each exterior angle of any regular polygon can be found by dividing 360 degrees by the number of sides of the polygon. In this case, a do-decagon has 12 sides, so each exterior angle measures 360/12 = 30 degrees.